Theorem ndsubsucc-P7.24a.RC 897

Description: Inference Form of ndsubsucc-P7.24a 851. †

Hypothesis

Ref	Expression
ndsubsucc-P7.24a.RC.1	⊢ 𝑡 = 𝑢

Assertion

Ref	Expression
ndsubsucc-P7.24a.RC	⊢ s‘𝑡 = s‘𝑢

Proof of Theorem ndsubsucc-P7.24a.RC

Step	Hyp	Ref	Expression
1		ndsubsucc-P7.24a.RC.1	. . . 4 ⊢ 𝑡 = 𝑢
2	1	ndtruei-P3.17 182	. . 3 ⊢ (⊤ → 𝑡 = 𝑢)
3	2	subsucc-P5 644	. 2 ⊢ (⊤ → s‘𝑡 = s‘𝑢)
4	3	ndtruee-P3.18 183	1 ⊢ s‘𝑡 = s‘𝑢

Syntax hints:  s‘term_succ 3   = wff-equals 6  ⊤wff-true 153

This theorem was proved from axioms:  ax-L1 11  ax-L2 12  ax-L3 13  ax-MP 14  ax-L9-succ 22

This theorem depends on definitions:  df-bi-D2.1 107  df-and-D2.2 133  df-true-D2.4 155

This theorem is referenced by: (None)